Approximate Coloring of Uniform Hypergraphs (Extended Abstract) [chapter]

Michael Krivelevich, Benny Sudakov
<span title="">1998</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of nding the exact value of the chromatic number of a hypergraph is known to be NP-hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r 3 it is impossible to approximate in polynomial time the chromatic number of r-uniform hypergraphs on n vertices within a factor n 1? for any > 0, unless NP ZPP. On the positive side,
more &raquo; ... present an approximation algorithm for coloring r-uniform hypergraphs on n vertices, whose performance ratio is O(n(log log n) 2 =(log n) 2 ). We also describe an algorithm for coloring 3-uniform 2-colorable hypergraphs on n vertices inÕ(n 9=41 ) colors, thus improving previous results of Chen and Frieze and of Kelsen, Mahajan and Ramesh.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/3-540-68530-8_40</a> <a target="_blank" rel="external noopener" href="">fatcat:qy3kpwszg5hcvaphb4emftewfm</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> </button> </a>